Abstract : In this paper, we have two objectives: First we model the posting behaviour of publishers in Social Networks which have externalities, and the second objective is to propose content active filtering in order to increase content diversity from different publishers. By externalities, we mean that when the quantity of posted contents from a specific publisher impacts the popularity of other posted contents. We introduce a dynamical model to describe the posting behaviour of publishers taking into account these externalities. Our model is based on stochastic approximations and sufficient conditions are provided to ensure its convergence to a unique rest point. We provide a close form of this rest point and show that it can be obtained as the unique equilibrium of a non-cooperative game. Content Active Filtering (CAF) are actions taken by the administrator of the Social Network in order to promote some objectives related to the quantity of contents posted in various contents. As objective of the CAF we shall consider maximizing the diversity of posted contents. Finally, we illustrate our results through numerical simulations and we validate them with real data extracted from social networks.